Problem: Solve for $x$ and $y$ using elimination. ${5x+5y = 45}$ ${-3x+6y = 18}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-6$ and the bottom equation by $5$ ${-30x-30y = -270}$ $-15x+30y = 90$ Add the top and bottom equations together. $-45x = -180$ $\dfrac{-45x}{{-45}} = \dfrac{-180}{{-45}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {5x+5y = 45}\thinspace$ to find $y$ ${5}{(4)}{ + 5y = 45}$ $20+5y = 45$ $20{-20} + 5y = 45{-20}$ $5y = 25$ $\dfrac{5y}{{5}} = \dfrac{25}{{5}}$ ${y = 5}$ You can also plug ${x = 4}$ into $\thinspace {-3x+6y = 18}\thinspace$ and get the same answer for $y$ : ${-3}{(4)}{ + 6y = 18}$ ${y = 5}$